Technical Report PHD-2010-13

Title: Multi Level Methods for Data Completion
Authors: Michal Holtzman Gazit
Supervisors: Irad Yavneh
Abstract: There are many cases where missing data needs to be completed in an image. The reasons for this, and the form of completion, vary from application to application. The solutions for most of these problems usually involve some local process that is applied to the image in order to restore the missing information. In this research we explore an approach that uses multiple levels of detail of the image in a novel way. This approach has an advantage over existing methods for two main reasons. First, examining all the scales of the image allows us to obtain a more global understanding of the problem. By doing so, we learn to handle both the fine details and the coarse information and aim to obtain a solution that is consistent over all levels of detail. In addition, multiple levels can sometimes be used to obtain faster convergence of the computational process. Our research is about a novel and rather fundamental principle: consistency with respect to scale. In our approach, the completed information must satisfy the criteria at all scales. Rather than following the coarse solution to the finer levels of detail, as is often done, all image versions agree on a single common solution. Thus, in effect, all the different versions guide all others. Moreover, all versions of our image are of the same size -- there is no "coarsening". Rather, we apply an edge-preserving smoothing out of details -- unlike any "coarsening" used previously for image completion. Scale thus plays the role of a third dimension of the image, with the multi-scale versions of the image keeping each other from straying off track.

We develop this approach in three different applications: completion of missing parts of images, detection of salient regions in images, and registration between images captured by different modalities. In each application we show how this approach can be used and demonstrate its advantage over existing methods.

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